A240224 Irregular triangular array read by rows: row n gives a list of the partitions of n into distinct Fibonacci numbers. The order of the partitions is like in Abramowitz-Stegun.

1, 2, 3, 2, 1, 3, 1, 5, 3, 2, 5, 1, 3, 2, 1, 5, 2, 8, 5, 3, 5, 2, 1, 8, 1, 5, 3, 1, 8, 2, 5, 3, 2, 8, 3, 8, 2, 1, 5, 3, 2, 1, 8, 3, 1, 13, 8, 5, 8, 3, 2, 13, 1, 8, 5, 1, 8, 3, 2, 1, 13, 2, 8, 5, 2, 13, 3, 13, 2, 1, 8, 5, 3, 8, 5, 2, 1, 13, 3, 1, 8, 5, 3, 1, 13, 5, 13, 3, 2, 8, 5, 3, 2, 13, 5, 1, 13, 3, 2, 1, 8, 5, 3, 2, 1, 13, 5, 2

Offset: 1

Author

Wolfdieter Lang, Apr 07 2014

Keywords

• nonn
• tabf

Comments

The row length sequence is A240225. The number of partitions in row n is A000119(n).

The order of the partitions is like in Abramowitz-Stegun (rising number of parts, within like part numbers lexicographic) but here the order of the parts has been reversed, that is they are ordered decreasingly.

Examples

			The array with separated partitions begins:
n\k       1         2          3         4            5 ...
1:        1
2:        2
3:        3       2,1
4:      3,1
5:        5       3,2
6:      5,1     3,2,1
7:      5,2
8:        8       5,3      5,2,1
9:      8,1     5,3,1
10:     8,2     5,3,2
11:     8,3     8,2,1    5,3,2,1
12:   8,3,1
13:      13       8,5      8,3,2
14:    13,1     8,5,1    8,3,2,1
15:    13,2     8,5,2
16:    13,3    13,2,1      8,5,3   8,5,2,1
17:  13,3,1   8,5,3,1
18:    13,5    13,3,2    8,5,3,2
19:  13,5,1  13,3,2,1  8,5,3,2,1
20:  13,5,2
21:      21      13,8     13,5,3  13,5,2,1
22:    21,1    13,8,1   13,5,3,1
23:    21,2    13,8,2   13,5,3,2
24:    21,3    21,2,1     13,8,3  13,8,2,1   13,5,3,2,1
25:  21,3,1  13,8,3,1
...
		

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A000119, A239001, A240225.